the first 3 terms of the sequence -8,x,y,72... form an arithmetic sequence while the 2nd 3rd and fourth terms form a geometric sequence. determine x and y
note: arithemtic : common difference
geometric: common ratio
thanks, this is suppperrrrr important:)
note: arithemtic : common difference
geometric: common ratio
thanks, this is suppperrrrr important:)
-
-8, x, y form arithmetic series
=> x + 8 = y - x
=> 2x = y - 8
x = (y/2) - 4 --------(1)
x, y, 72 are in geometric series
=> y/x = 72/y
=> y^2 = 72x
substitute x value from (1)
=> y^2 = 72 (y/2 - 4)
=> y^2 = 36y - 288
=> y^2 - 36y + 288 = 0
=> (y - 24)(y - 12) = 0
y = 12 and 24
x = (y/2) - 4
x = 2 and 8
The arithmetic sequences are
-8, 2, 12 with d = 10 and -8, 8, 24 with d = 16
The geometric sequences are
2, 12, 72 with r = 6 and 8, 24, 72 with r = 3
=> x + 8 = y - x
=> 2x = y - 8
x = (y/2) - 4 --------(1)
x, y, 72 are in geometric series
=> y/x = 72/y
=> y^2 = 72x
substitute x value from (1)
=> y^2 = 72 (y/2 - 4)
=> y^2 = 36y - 288
=> y^2 - 36y + 288 = 0
=> (y - 24)(y - 12) = 0
y = 12 and 24
x = (y/2) - 4
x = 2 and 8
The arithmetic sequences are
-8, 2, 12 with d = 10 and -8, 8, 24 with d = 16
The geometric sequences are
2, 12, 72 with r = 6 and 8, 24, 72 with r = 3